In semiconductors at usual temperatures, the concentration of carriers (electrons or holes) is essentially determined by the concentration and distribution of the dopants present in the semiconductor. Other impurities, depending on their density relative to the dopant concentration, may have a secondary effect on the carrier concentration. For each case, the distribution of carrier concentration is determined by the actual boundary conditions, such as the bias on the semiconductor sample, and the actual charge density values in the states of the external and internal interfaces.
Current technologies usually provide semiconductor materials and structures in which the impurity levels are considerably below the dopant concentrations, and the interface state densities are negligible. Therefore, the dielectrical properties of common semiconductor materials, e.g. silicon, gallium arsenide, are in good agreement with the properties of an "ideal" material in which the conductivity and carrier density vary with the location, whereas the dielectrical constant is not frequency dependent.
The basic methods used for testing semiconductor structures containing one space charge layer, manufactured from such semiconductors materials, are directly or indirectly based on the measurement of capacitance as a function of voltage, and are usually performed in the 1 Hz to 1 MHz frequency range. The upper limit of the frequency is determined by the values of the resistances connected in series with the capacitance of the interface or pn junction to be measured (including those of the sample and the contact), the effect of the radiation increasing parallel with the frequency increase, and the technical difficulties usually associated with high-frequency measurements. The lower measuring frequency is limited by an unavoidable increase in the measuring time, the insulation resistances which become more critical at lower frequencies, and the effect of the deep level impurities present in the sample, which are only capable of a slow response and are, therefore, measured only below a certain lower frequency limit.
There are a number of methods known in the art for determining the carrier concentration and its distribution as a function of depth in semiconductors. However, those with practical applicability are usually based on capacitance measurement.
These measurements require two electrical contacts: a so called ohmic contact the impedance of which is negligible relative to the impedance of the capacitance of the sample measured at the applied frequency or frequencies, and a so called rectifying (barrier) contact, having the current-voltage characteristics of a diode and resulting in a substantially higher transition resistance than the impedance of the sample to be measured at the test frequency (frequencies). These contacts may also be formed in nondestructive ways, such as by using a mercury electrode or forming an electrode by contacting an electrolyte with the semiconductor sample.
According to the simplest approach, the capacitance-voltage characteristics of the sample are recorded, and the results are numerically evaluated by a computer [see, e.g. Thomas, C.O. et al., J. Electrochem. Soc. 109, 1055-1061 (1962)].
This method is very inaccurate and is entirely unsuitable for testing structures having unstable electrical parameters or characteristics, or manufactured from materials containing large amounts of impurities and/or internal interfaces which can not follow the measuring frequency but follow the change in the bias when recording the capacitance-voltage characteristics.
To avoid these problems, and to produce a voltage signal directly proportional with the carrier concentration (sometimes on a logarithmic scale) so called modulation-type measuring techniques have been developed. In this case, in addition to the bias, a high-frequency measuring signal and a so called modulation signal are applied to the sample, the latter having orders of magnitude lower frequency than the measuring signal. An essential feature of this approach is that first the measuring signal and the most important modulation products produced by the nonlinearity of the sample, i.e. the products the frequencies of which equal to the sum and to the difference of the two frequencies (measuring signal and modulation frequencies) are amplified and rectified, followed by further amplification and rectification of the low frequency components of the rectified signal, the frequency of which is the same as the frequency of the modulation signal. The method to develop the modulation signal by repeated amplification and rectification explains the big difference between the measuring signal and modulation signal frequencies.
In both rectification steps usually phase-sensitive rectifiers are employed. The final signal is proportionate with the derivative of the capacitance-characteristic as a function of voltage (gradient), from which (knowing the capacitance, the surface of the sample, and the dielectrical constant of the sample material) the local value of the carrier concentration can be determined. If the measurement is performed by changing the bias, it is possible to determine the carrier concentration profile in a range with margins determined by the sample parameters. (The maximum depth is usually limited by the breakdown voltage of the rectifying contact, which can be exceeded only by destructive techniques, removing part of the sample material.) The carrier concentration is provided by analog or digital circuits and techniques.
These methods exist in numerous variations, differing in various technical details, including the manner of applying the bias and the measuring and modulating signals to the sample (voltage or current generator mode), and the actual techniques used for control of the amplitude of the a.c. signals according to the actual signal measured, etc. The main purpose of these variations is to provide the required information in a form convenient for the user, and in a form that is easy to record on an x-y recorder.
Such measuring techniques are for example, disclosed by Califano, F.P. and Luciano, A., The Rev. of Sci. Instr. 41, 865-869 (1970); Gordon, B.J. et al.: A new impurity profile plotter for epitaxy and device. Silicon Device Conf. Gaithersburg, Md., 1970; Baxandall, P.J. et al., J. of Physics E. 4, 213-221 (1971). In a typical embodiment, Faktor, M.M. et al. (U. K. Patent No. 1,482,929 and its U.S. equivalents Nos. 4,168,212 and 4,028,207), formed the rectifying contact by contacting a semiconductor with an electrolyte, and performed the measurement by using a 3 kHz measuring signal and a 30 Hz modulation signal.
The technique described by Copeland, J. A., IEEE Trans. on El. Dev. ED-16, 445-449 (1969) is based on a different principle. Only one measuring voltage is applied to the sample, and, as a result of the sample non-linearity, the current transported through the sample includes the harmonics of the measuring signal. The amplitude of the second harmonic can be considered as a derivative of the capacitance-voltage characteristic as a function of the high frequency voltage of the sample, from which the carrier concentration can be calculated. A necessary condition for the successful application of this technique is the use of a measuring signal free of the second harmonic.
The practical applicability of these techniques is limited. The problem usually is that when the semiconductor materials and structures are heavily contaminated or when instable (often unreproducible) contacts are employed (such are the electrolytesemi-conductor contacts), the capacitance-voltage characteristic and the carrier concentration distribution are not reproducible, therefore, the reliability of these techniques is not satisfactory. Apart from the exceptionally good-quality semiconductor materials, the above-mentioned disturbing effects are negligible only within a relatively narrow frequency range. The actual limits of this frequency range vary for different semiconductor materials. (The samples for which such a range can not be found, are considered unsuitable for characterization.)